A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000 - IEEE Signal Processing Magazine

The JPEG committee has recently released its new image coding standard, JPEG 2000, which will serve as a supplement for the original JPEG standard introduced in 1992. Rather than incrementally improving on the original standard, JPEG 2000 implements an entirely new way of compressing images based on the wavelet transform, in contrast to the discrete cosine transform (DCT) used in the original JPEG standard. The significant change in coding methods between the two standards leads one to ask: What prompted the JPEG committee to adopt such a dramatic change? The answer to this question comes from considering the state of image coding at the time the original JPEG standard was being formed. At that time wavelet analysis and wavelet coding were still very new technologies, whereas DCT-based transform techniques were well established. Early wavelet coders had performance that was at best comparable to transform coding using the DCT. The comparable performance between the two methods, coupled with the considerable momentum already behind DCT-based transform coding, led the JPEG committee to adopt DCT-based transform coding as the foundation of the lossy JPEG standard. The state of wavelet-based coding has improved significantly since the introduction of the original JPEG standard. A notable breakthrough was the introduction of embedded zero-tree wavelet (EZW) coding by Shapiro [1]. The EZW algorithm was able to exploit the multiresolutional properties of the wavelet transform to give a computationally simple algorithm with outstanding performance. Improvements and enhancements to the EZW algorithm have resulted in modern wavelet coders which have improved performance relative to block transform coders. As a result, wavelet-based coding has been adopted as the underlying method to implement the JPEG 2000 standard. Prior to JPEG 2000, wavelet-based coding was mainly of interest to a limited number of compression researchers. Since the new JPEG standard is wavelet based, a much larger audience including hardware designers, software programmers, and systems designers will be interested in wavelet-based coding. One of the purposes of this article is to give a general audience sufficient background into the details and techniques of wavelet coding to better understand the JPEG 2000 standard. The focus of this discussion is on the fundamental principles of wavelet coding and not the actual standard itself (more details on the standard can be found in [2]). Part of this discussion will try to explain some of the confusing design choices made in wavelet coders. For example, those familiar with wavelet analysis know that there are two types of f i l ter choices: orthogonal and biorthogonal [3]-[5]. Orthogonal filters have the nice property that they are energy or norm preserving and in this aspect are similar to the DCT transform. Nevertheless, modern wavelet coders use biorthogonal filters which do not preserve energy. Another peculiarity of wavelet coders is that the wavelet transform can use essentially an infinite number of possible biorthogonal (or orthogonal) filters. Nevertheless, only a very small number of filter sets, often one or two, are used in practice. Reasons for these specific design choices will be explained.